Two nonidentical atoms may be entangled by inducing simultaneous cooperative absorption of a photon pair from a light field that is nonresonant to either atom in isolation. The atoms may be of two different elements, of different isotopes of the same element, or of a single isotope undergoing different transitions. Utilizing this cooperative process, we propose a protocol for a conditional operation with neutral atoms in an optical lattice. Current practical capabilities permit execution of the scheme.